    In this section, we obtain the relationship between \(\mathcal {H}_{\mu ,\alpha }\)  and \(\mathcal {I}_{\mu ,\alpha }\) . We also obtain a necessary condition such that \(\mathcal {H}_{\mu ,\alpha }\)  is a bounded operator acting on Bloch type spaces for general cases. Then we characterize the measures \(\mu \)  for which the operator \(\mathcal {H}_{\mu ,\alpha }\)  (\(\alpha \ge 2\) ) is bounded (resp. compact) from Bloch type spaces into \({B}_{\alpha -1}\) . We begin with describing for which measures \(\mu \)  the operator \(\mathcal {H}_{\mu ,\alpha }\)  is well defined on the Bergman space \(A^p\)  (\(0<p<\infty \) ), which is a generalization of Theorem 2.1 in [1]}.
